slaapzak
50 ( +1 | -1 )well, both rook + bishop vs rook (90% of the cases) and rook + knight vs. rook (less chance though) are won on average, but these endgames are very difficult. even grand masters play rook vs. bishop on, and most of the times it becomes a draw.

rook + two minor pices vs. two rooks it depends on which pieces are the two minors I think. the position will also matter whether exchanging helps or not. two bishops + a rook for instance have a lot of mating potential for instance.

atrifix
78 ( +1 | -1 )WellKRB vs. KR and KRN vs. KR are usually drawn, not won, but sometimes people will play on. There are winning positions for each, but most of the time when you see these endgames in practice they are draws. However, KRB vs. KR is somewhat difficult to draw, particularly if you don't know the theory.

In the general cases, however, when one side has 2 rooks vs. rook + 2 minor pieces, or if a side has 2 rooks vs. rook + one minor piece (by exchange sac), it is usually beneficial to the side with the rooks to exchange one pair of rooks. This is because the rooks have great maneuvering ability and the playor with the minor piece(s) will be unable to compete as easily on ranks and files. In the endgames, this rule sometimes changes, because with reduced material it becomes more difficult to win games.

slaapzak
38 ( +1 | -1 )sry atrifix, you are a great player, but I can't agree with you on one point.

endgame tables have proven rook+bishop vs. rook is won. it is just too difficult for the human mind, to win it, because you have to play some really strange looking moves. the computer doesn't use the theory, and that helps the computer, because theory doesn't always give the best moves.

atrifix
159 ( +1 | -1 )KRB vs. KRThis is simply not correct. First, a simple endgame tablebase is hardly too complex for the human mind--humans have memorized numbers like pi and entire volumes of books, so why not a move list? Second, if the endgame tablebases produce a result that differs from theory, then the theory is changed; people don't just continue playing with bad theory. It is true that computer-generated tablebases have refined some of the endgame theories (KQ vs. KR is probably the most notable), but to my knowledge there has been no effect on KRB vs. KR, and it certainly has not changed the result.

Again, KRB vs. KR can be won or drawn depending on the initial position of the pieces, but in the majority of cases when it occurs in practice, it is drawn (KRN vs. KR can also be won or drawn, but this is almost always drawn). If you don't believe me, check an endgame tablebase, or generate your own. Even if you are aware of the theory, however, the endgame is notoriously difficult to hold.

W: Kd6, Bg4, Re2 B: Ka8, Rh7 White wins in 65 with 1. Bf5. Under FIDE laws, this would be a draw under the 50-move rule, but few players can defend this position perfectly, so White has excellent practical chances to win (of course, on the other hand, few players can mate perfectly).

W: Ke2, Be6, Rb2 B: Ka8, Rg1 Drawn no matter what White does. There may still be practical chances to win.

To clarify, my previous post about competing on ranks and files was referring to endgames when pawns are still on the board.

fmgaijin
44 ( +1 | -1 )Am I Confused, Or . . .Didn't the original post ask about 2R vs. R+2 minors, wondering who benefitted from a R exchange? To answer THAT question, it depends the activity of the remaining R. In general, the 2R side is worse off to begin with (2 minors being better than a R or R + P most of the time) and hence should generally avoid exchanges, BUT if the R exchange allows the remaining R to become active and tie down the pieces to defending Ps, then it would be a good idea to exchange.